2010/03/17 by Jakob Kellner, Saharon Shelah · 1 citation
Computer Science · Mathematics · #Advanced Topology and Set Theory #Combinatorics #Computability, Logic, AI Algorithms #Continuum hypothesis #Discrete mathematics #Existential quantification #Forcing (mathematics) #Limits and Structures in Graph Theory #Mathematical analysis #Mathematics #Omega #Physics #Quantum mechanics #Tree (set theory) #math.LO #msc:03E17 #msc:03E40
paper · pdf · doi:10.1007/s00153-011-0253-8
published as Arch. Math. Logic 51 (2012), No. 1-2, 49-70
arxiv created 2010/03/17 · openalex publication_date 2011/11/03 · arxiv updated 2012/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
For f,g∈ωω let c^∀f,g be the minimal number of uniform g-splitting trees needed to cover the uniform f-splitting tree, i.e., for every branch ν of the f-tree, one of the g-trees contains ν. Let c^∃f,g be the dual notion: For every branch ν, one of the g-trees guesses ν(m) infinitely often. We show that it is consistent that c^∃fε,gε=c^∀fε,gε=κε for continuum many pairwise different cardinals κε and suitable pairs (fε,gε). For the proof we introduce a new mixed-limit creature forcing construction.